def test_equation_validate(self):
""" Test the error checking within the solve() function """
model = Model()
model.var('x')
with self.assertRaises(EquationError) as context:
model.solve()
self.assertEquals('under-specified', context.exception.errorid)
def test_set_var_default(self):
""" Test the set_var_default """
model = Model()
var = model.var('test')
self.assertEquals(None, var.default)
model.set_var_default(12)
var = model.var('test2')
self.assertEquals(12, var.default)
def test_series_get_at_errors(self):
""" Test bad parameters to get_at """
model = Model()
varx = model.var('x')
vary = model.var('y')
with self.assertRaises(EquationError):
model.get_at(varx, vary)
def test_series_get_at_errors(self):
""" Test bad parameters to get_at """
model = Model()
varx = model.var('x')
vary = model.var('y')
with self.assertRaises(EquationError):
model.get_at(varx, vary)
def test_param_default(self):
""" Test the set_param_default """
model = Model()
param = model.param('test')
self.assertEquals(None, param.default)
model.set_param_default(122)
param = model.param('test2')
self.assertEquals(122, param.default)
def test_rule_with_coefficients(self):
""" Test creating rules with simple coefficents """
model = Model()
model.var('x')
model.var('y')
model.add('2*x = 3*y')
self.assertEquals(2, len(model.variables))
self.assertEquals(0, len(model.parameters))
def test_series_derivative(self):
model = Model()
varx = model.var('x')
vary = model.var('y')
equation = model.add('x = y + x(-1)')
df = equation.expr.diff(varx)
self.assertEquals(0, df)
df = equation.expr.diff(vary)
self.assertEquals(1, df)
def test_evaluate_series_access(self):
""" Test evaluation with series accessor """
model = Model()
model.var('x', default=1)
model.var('y', default=10)
model.param('a', default=.5)
model.solutions = [{'x': 2, 'y': 11, 'a': 60}]
self.assertEquals(11, model.evaluate('y(-1)'))
self.assertEquals(73, model.evaluate('x(-1) + y(-1) + a(-1)'))
def test_calling_sympy_functions(self):
""" Test the calling of sympy functions """
model = Model()
model.var('x')
model.param('a')
model.set_values({'x': 12, 'a': 5})
self.assertEquals(1.1, model.evaluate('Max(1, 1.1)'))
def test_calculation_error(self):
""" Test an error while calculating """
model = Model()
model.var('y', default=0)
model.var('x', default=0)
model.add('y = 2/x')
model.add('x = 12')
with self.assertRaises(CalculationError) as context:
model.solve(iterations=10, threshold=1e-4)
self.assertTrue(isinstance(context.exception.inner, ZeroDivisionError))
def test_evaluate(self):
""" Test arbitrary function evaluation """
model = Model()
model.var('x', default=1)
model.var('y', default=10)
model.param('a', default=.5)
self.assertEquals(11, model.evaluate('x+y'))
def test_rule(self):
""" Test creating rules """
model = Model()
model.var('x')
model.var('y')
eqn = model.add('x = y')
self.assertEquals(2, len(model.variables))
self.assertEquals(0, len(model.parameters))
self.assertIsNotNone(model.variables['x'].equation)
self.assertIsNone(model.variables['y'].equation)
self.assertEquals(1, len(model.equations))
self.assertEquals(eqn, model.equations[0])
def test_rule(self):
""" Test creating rules """
model = Model()
model.var('x')
model.var('y')
eqn = model.add('x = y')
self.assertEquals(2, len(model.variables))
self.assertEquals(0, len(model.parameters))
self.assertIsNotNone(model.variables['x'].equation)
self.assertIsNone(model.variables['y'].equation)
self.assertEquals(1, len(model.equations))
self.assertEquals(eqn, model.equations[0])
def test_delta_error(self):
model = Model()
model.var('x', default=-1)
model.var('y', default=10)
model.param('a', default=.5)
model.solutions = [{'x': 2, 'y': 11, 'a': 60}]
model.variables['x'].value = 5
with self.assertRaises(EquationError) as context:
model.evaluate('d(-1)')
self.assertEquals('d-arg-not-a-variable', context.exception.errorid)
def test_calculation_error(self):
""" Test an error while calculating """
model = Model()
model.var('y', default=0)
model.var('x', default=0)
model.add('y = 2/x')
model.add('x = 12')
with self.assertRaises(CalculationError) as context:
model.solve(iterations=10, threshold=1e-4)
self.assertTrue(isinstance(context.exception.inner, ZeroDivisionError))
def test_set_parameters_equation(self):
""" Test set_values of parameters using equations """
model = Model()
model.param('a', default=-1)
model.var('x', default=0)
model.set_values({'a': 'x+12'})
self.assertEquals(12, model.parameters['a'].value)
def test_set_variables_equation(self):
""" Test set_values of variables using equations """
model = Model()
model.param('a', default=-1)
model.var('x', default=0)
model.set_values({'x': 'a+12'})
self.assertEquals(11, model.variables['x'].value)
def test_evaluate(self):
""" Test arbitrary function evaluation """
model = Model()
model.var('x', default=1)
model.var('y', default=10)
model.param('a', default=.5)
self.assertEquals(11, model.evaluate('x+y'))
def test_model_failure(self):
""" Test for divergence """
model = Model()
model.var('x', default=1.1)
model.var('y', default=2.3)
model.add('2*x = 11 - 3*y')
model.add('7*y = 13 - 5*x')
with self.assertRaises(SolutionNotFoundError):
model.solve(iterations=100, threshold=1e-4)
def test_delta(self):
""" test the d() function """
model = Model()
model.var('x', default=-1)
model.var('y', default=10)
model.param('a', default=.5)
model.solutions = [{'x': 2, 'y': 11, 'a': 60}]
model.variables['x'].value = 5
self.assertEquals(3, model.evaluate('d(x)'))
def test_series_get_at(self):
""" Test the series accessor creation, get_at() """
model = Model()
varx = model.var('x')
param = model.get_at(varx, 0)
self.assertIsNotNone(param)
self.assertEquals('_x_0', param.name)
self.assertEquals(0, param.iteration)
self.assertEquals(varx, param.variable)
self.assertTrue(param.name in model._private_parameters)
param = model.get_at(varx, 1)
self.assertIsNotNone(param)
self.assertEquals('_x_1', param.name)
self.assertEquals(1, param.iteration)
self.assertEquals(varx, param.variable)
self.assertTrue(param.name in model._private_parameters)
param = model.get_at(varx, -1)
self.assertIsNotNone(param)
self.assertEquals('_x__1', param.name)
self.assertEquals(-1, param.iteration)
self.assertEquals(varx, param.variable)
self.assertTrue(param.name in model._private_parameters)
param = model.get_at(varx, 10000)
self.assertIsNotNone(param)
self.assertEquals('_x_10000', param.name)
self.assertEquals(10000, param.iteration)
self.assertEquals(varx, param.variable)
self.assertTrue(param.name in model._private_parameters)
def test_if_true(self):
""" Test the if_true builtin function """
model = Model()
model.var('x', default=12)
model.var('y', default=3131)
self.assertEquals(0, model.evaluate('if_true(x > 1000)'))
self.assertEquals(1, model.evaluate('if_true(y > 1000)'))
def test_setting_multiple_variables(self):
""" Test set_values() with multiple variables """
model = Model()
model.param('a', default=3)
model.param('b', default=4)
model.var('x', default=-1)
model.var('y', default=-2)
model.set_values({'a': 'a+11', 'b': '4*b'})
self.assertEquals(14, model.parameters['a'].value)
self.assertEquals(16, model.parameters['b'].value)
def test_set_variables_equation(self):
""" Test set_values of variables using equations """
model = Model()
model.param('a', default=-1)
model.var('x', default=0)
model.set_values({'x': 'a+12'})
self.assertEquals(11, model.variables['x'].value)
def test_set_parameters_equation(self):
""" Test set_values of parameters using equations """
model = Model()
model.param('a', default=-1)
model.var('x', default=0)
model.set_values({'a': 'x+12'})
self.assertEquals(12, model.parameters['a'].value)
def test_model_failure(self):
""" Test for divergence """
model = Model()
model.var('x', default=1.1)
model.var('y', default=2.3)
model.add('2*x = 11 - 3*y')
model.add('7*y = 13 - 5*x')
with self.assertRaises(SolutionNotFoundError):
model.solve(iterations=100, threshold=1e-4)
def test_set_variables(self):
""" Test set_values of variables """
model = Model()
var_x = model.var('x', default=-1)
self.assertEquals(-1, var_x.value)
model.set_values({'x': 22})
self.assertEquals(22, var_x.value)
with self.assertRaises(ValueError):
model.set_values({'zz': -1})
def test_set_parameters(self):
""" Test set_values of parameters """
model = Model()
param_a = model.param('a', default=-1)
self.assertEquals(-1, param_a.value)
model.set_values({'a': 22})
self.assertEquals(22, param_a.value)
with self.assertRaises(ValueError):
model.set_values({'zz': -1})
def test_equation_validate(self):
""" Test the error checking within the solve() function """
model = Model()
model.var('x')
with self.assertRaises(EquationError) as context:
model.solve()
self.assertEquals('under-specified', context.exception.errorid)
def test_if_true(self):
""" Test the if_true builtin function """
model = Model()
model.var('x', default=12)
model.var('y', default=3131)
self.assertEquals(0, model.evaluate('if_true(x > 1000)'))
self.assertEquals(1, model.evaluate('if_true(y > 1000)'))
def test_series_get_at(self):
""" Test the series accessor creation, get_at() """
model = Model()
varx = model.var('x')
param = model.get_at(varx, 0)
self.assertIsNotNone(param)
self.assertEquals('_x_0', param.name)
self.assertEquals(0, param.iteration)
self.assertEquals(varx, param.variable)
self.assertTrue(param.name in model._private_parameters)
param = model.get_at(varx, 1)
self.assertIsNotNone(param)
self.assertEquals('_x_1', param.name)
self.assertEquals(1, param.iteration)
self.assertEquals(varx, param.variable)
self.assertTrue(param.name in model._private_parameters)
param = model.get_at(varx, -1)
self.assertIsNotNone(param)
self.assertEquals('_x__1', param.name)
self.assertEquals(-1, param.iteration)
self.assertEquals(varx, param.variable)
self.assertTrue(param.name in model._private_parameters)
param = model.get_at(varx, 10000)
self.assertIsNotNone(param)
self.assertEquals('_x_10000', param.name)
self.assertEquals(10000, param.iteration)
self.assertEquals(varx, param.variable)
self.assertTrue(param.name in model._private_parameters)
def test_param_default(self):
""" Test the set_param_default """
model = Model()
param = model.param('test')
self.assertEquals(None, param.default)
model.set_param_default(122)
param = model.param('test2')
self.assertEquals(122, param.default)
def test_set_var_default(self):
""" Test the set_var_default """
model = Model()
var = model.var('test')
self.assertEquals(None, var.default)
model.set_var_default(12)
var = model.var('test2')
self.assertEquals(12, var.default)
def test_rule_with_coefficients(self):
""" Test creating rules with simple coefficents """
model = Model()
model.var('x')
model.var('y')
model.add('2*x = 3*y')
self.assertEquals(2, len(model.variables))
self.assertEquals(0, len(model.parameters))
def test_param(self):
""" Test parameter creation """
model = Model()
param_x = model.param('x')
self.assertIsNotNone(param_x)
with self.assertRaises(DuplicateNameError):
model.var('x')
with self.assertRaises(DuplicateNameError):
model.param('x')
self.assertTrue('x' not in model.variables)
self.assertTrue('x' in model.parameters)
def test_set_variables(self):
""" Test set_values of variables """
model = Model()
var_x = model.var('x', default=-1)
self.assertEquals(-1, var_x.value)
model.set_values({'x': 22})
self.assertEquals(22, var_x.value)
with self.assertRaises(ValueError):
model.set_values({'zz': -1})
def test_set_parameters(self):
""" Test set_values of parameters """
model = Model()
param_a = model.param('a', default=-1)
self.assertEquals(-1, param_a.value)
model.set_values({'a': 22})
self.assertEquals(22, param_a.value)
with self.assertRaises(ValueError):
model.set_values({'zz': -1})
def test_param(self):
""" Test parameter creation """
model = Model()
param_x = model.param('x')
self.assertIsNotNone(param_x)
with self.assertRaises(DuplicateNameError):
model.var('x')
with self.assertRaises(DuplicateNameError):
model.param('x')
self.assertTrue('x' not in model.variables)
self.assertTrue('x' in model.parameters)
def test_update_solutions(self):
""" Test _update_solutions function """
model = Model()
varx = model.var('x')
vary = model.var('y')
model._update_solutions({'x': 1.1, 'y': 2.2})
self.assertEquals(1, len(model.solutions))
self.assertEquals(1.1, varx.value)
self.assertTrue('x' in model.solutions[0])
self.assertEquals(1.1, model.solutions[0]['x'])
self.assertEquals(2.2, vary.value)
self.assertTrue('y' in model.solutions[0])
self.assertEquals(2.2, model.solutions[0]['y'])
model._update_solutions({'x': 3.3, 'y': 4.4})
self.assertEquals(2, len(model.solutions))
self.assertEquals(3.3, varx.value)
self.assertTrue('x' in model.solutions[1])
self.assertEquals(3.3, model.solutions[1]['x'])
self.assertEquals(4.4, vary.value)
self.assertTrue('y' in model.solutions[1])
self.assertEquals(4.4, model.solutions[1]['y'])
def test_update_solutions(self):
""" Test _update_solutions function """
model = Model()
varx = model.var('x')
vary = model.var('y')
model._update_solutions({'x': 1.1, 'y': 2.2})
self.assertEquals(1, len(model.solutions))
self.assertEquals(1.1, varx.value)
self.assertTrue('x' in model.solutions[0])
self.assertEquals(1.1, model.solutions[0]['x'])
self.assertEquals(2.2, vary.value)
self.assertTrue('y' in model.solutions[0])
self.assertEquals(2.2, model.solutions[0]['y'])
model._update_solutions({'x': 3.3, 'y': 4.4})
self.assertEquals(2, len(model.solutions))
self.assertEquals(3.3, varx.value)
self.assertTrue('x' in model.solutions[1])
self.assertEquals(3.3, model.solutions[1]['x'])
self.assertEquals(4.4, vary.value)
self.assertTrue('y' in model.solutions[1])
self.assertEquals(4.4, model.solutions[1]['y'])
# ###### Preliminaries # In order to build the model, we must first start off by importing several modules that will be used to build the model. *pysolve* is a Python module that I have developed to make it easier to specify and solve linear models. # # The first line will import the main Model class. The second line imports several utility functions that will prove useful. # In[2]: # ###### Create the model # The first step when developing a pysolve model is to create the model. This is just an empty model for now, but we will be adding the rest of the information to this. # In[3]: model = Model() # ###### Define the variables # The second step is to define the (endogenous) variables. These are the variables that we are allowed to manipulate within the model. This is pretty straigtforward. # # As a useful step, I define the default value for all variables. This can be changed on an individual basis. This is the value that the variable will start off with if nothing is changed. # In[4]: model.set_var_default(0) # Next, we create the variables used by the sim. Most of these have been explained above. # In[5]:
def create_simex_model():
""" Create the SIMEX model """
model = Model()
model.set_var_default(0)
model.var('Cd', desc='Consumption goods demand by households')
model.var('Cs', desc='Consumption goods supply')
model.var('Gs', desc='Government goods, supply')
model.var('Hd', desc='Cash money demanded by households')
model.var('Hh', desc='Cash money held by households')
model.var('Hs', desc='Cash money supplied by the government')
model.var('Nd', desc='Demand for labor')
model.var('Ns', desc='Supply of labor')
model.var('Td', desc='Taxes, demand')
model.var('Ts', desc='Taxes, supply')
model.var('Y', desc='Income = GDP')
model.var('YD', desc='Disposable income of households')
model.var('YDe', desc='Expected disposable income')
model.set_param_default(0)
model.param('Gd', desc='Government goods, demand')
model.param('W', desc='Wage rate')
model.param('alpha1', desc='Propensity to consume out of income')
model.param('alpha2', desc='Propensity to consume o of wealth')
model.param('theta', desc='Tax rate')
model.add('Cs = Cd') # 3.1
model.add('Gs = Gd') # 3.2
model.add('Ts = Td') # 3.3
model.add('Ns = Nd') # 3.4
model.add('YD = (W*Ns) - Ts') # 3.5
model.add('Td = theta * W * Ns') # 3.6, theta < 1.0
model.add('Cd = alpha1*YDe + alpha2*Hh(-1)') # 3.7E
model.add('Hs - Hs(-1) = Gd - Td') # 3.8
model.add('Hh - Hh(-1) = YD - Cd') # 3.9
model.add('Hd - Hs(-1) = YDe - Cd') # 3.18
model.add('Y = Cs + Gs') # 3.10
model.add('Nd = Y/W') # 3.11
model.add('YDe = YD(-1)') # 3.20
return model
def test_broyden(self):
""" Test solving with Broyden's method, instead of the
default Gauss-Seidel
"""
# pylint: disable=too-many-statements
model = Model()
model.set_var_default(0)
model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs',
'Cd', 'Ns', 'Nd')
model.set_param_default(0)
Gd = model.param('Gd')
W = model.param('W')
alpha1 = model.param('alpha1')
alpha2 = model.param('alpha2')
theta = model.param('theta')
model.add('Cs = Cd')
model.add('Gs = Gd')
model.add('Ts = Td')
model.add('Ns = Nd')
model.add('YD = (W*Ns) - Ts')
model.add('Td = theta * W * Ns')
model.add('Cd = alpha1*YD + alpha2*Hh(-1)')
model.add('Hs - Hs(-1) = Gd - Td')
model.add('Hh - Hh(-1) = YD - Cd')
model.add('Y = Cs + Gs')
model.add('Nd = Y/W')
# setup default parameter values
Gd.value = 20.
W.value = 1.0
alpha1.value = 0.6
alpha2.value = 0.4
theta.value = 0.2
debuglist = []
model.solve(iterations=100,
threshold=1e-4,
debuglist=debuglist,
method='broyden')
soln = round_solution(model.solutions[-1], decimals=1)
print(soln)
self.assertTrue(numpy.isclose(38.5, soln['Y']))
self.assertTrue(numpy.isclose(7.7, soln['Ts']))
self.assertTrue(numpy.isclose(30.8, soln['YD']))
self.assertTrue(numpy.isclose(18.5, soln['Cs']))
self.assertTrue(numpy.isclose(12.3, soln['Hs']))
self.assertTrue(numpy.isclose(12.3, soln['Hh']))
self.assertTrue(numpy.isclose(0, soln['_Hs__1']))
self.assertTrue(numpy.isclose(0, soln['_Hh__1']))
def test_full_model(self):
""" Test by implementing a model
This model is taken from the book
Monetary Economics 2ed, Godley and Lavoie, 2012
Chapter 3, The Simplest Model wtih Government Money
Model SIM
"""
# pylint: disable=too-many-statements
model = Model()
model.set_var_default(0)
model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs',
'Cd', 'Ns', 'Nd')
model.set_param_default(0)
Gd = model.param('Gd')
W = model.param('W')
alpha1 = model.param('alpha1')
alpha2 = model.param('alpha2')
theta = model.param('theta')
model.add('Cs = Cd')
model.add('Gs = Gd')
model.add('Ts = Td')
model.add('Ns = Nd')
model.add('YD = (W*Ns) - Ts')
model.add('Td = theta * W * Ns')
model.add('Cd = alpha1*YD + alpha2*Hh(-1)')
model.add('Hs - Hs(-1) = Gd - Td')
model.add('Hh - Hh(-1) = YD - Cd')
model.add('Y = Cs + Gs')
model.add('Nd = Y/W')
# setup default parameter values
Gd.value = 20.
W.value = 1.0
alpha1.value = 0.6
alpha2.value = 0.4
theta.value = 0.2
model.solve(iterations=200, threshold=1e-3)
soln = round_solution(model.solutions[-1], decimals=1)
self.assertTrue(numpy.isclose(38.5, soln['Y']))
self.assertTrue(numpy.isclose(7.7, soln['Ts']))
self.assertTrue(numpy.isclose(30.8, soln['YD']))
self.assertTrue(numpy.isclose(18.5, soln['Cs']))
self.assertTrue(numpy.isclose(12.3, soln['Hs']))
self.assertTrue(numpy.isclose(12.3, soln['Hh']))
self.assertTrue(numpy.isclose(0, soln['_Hs__1']))
self.assertTrue(numpy.isclose(0, soln['_Hh__1']))
model.solve(iterations=200, threshold=1e-3)
soln = round_solution(model.solutions[-1], decimals=1)
self.assertTrue(numpy.isclose(47.9, soln['Y']))
self.assertTrue(numpy.isclose(9.6, soln['Ts']))
self.assertTrue(numpy.isclose(38.3, soln['YD']))
self.assertTrue(numpy.isclose(27.9, soln['Cs']))
self.assertTrue(numpy.isclose(22.7, soln['Hs']))
self.assertTrue(numpy.isclose(22.7, soln['Hh']))
self.assertTrue(numpy.isclose(12.3, soln['_Hs__1']))
self.assertTrue(numpy.isclose(12.3, soln['_Hh__1']))
# Now run until the solutions themselves converge
prev_soln = model.solutions[-1]
converges = False
for _ in range(100):
model.solve(iterations=100, threshold=1e-3)
# run until we converge
soln = model.solutions[-1]
if is_close(prev_soln, soln, atol=1e-3):
converges = True
break
prev_soln = soln
self.assertTrue(converges)
prev = round_solution(model.solutions[-2], decimals=1)
soln = round_solution(model.solutions[-1], decimals=1)
self.assertTrue(numpy.isclose(100, soln['Y']))
self.assertTrue(numpy.isclose(20, soln['Ts']))
self.assertTrue(numpy.isclose(80, soln['YD']))
self.assertTrue(numpy.isclose(80, soln['Cs']))
self.assertTrue(numpy.isclose(0, soln['Hs'] - prev['Hs']))
self.assertTrue(numpy.isclose(0, soln['Hh'] - prev['Hh']))
def test_model_with_function(self):
""" Test model with builtin function call test """
model = Model()
model.var('x', default=0)
model.var('y', default=0)
model.add('2*x = 12 - y')
model.add('y = if_true(x > 10) + 5')
model.solve(iterations=10, threshold=1e-4)
self.assertEquals(2, len(model.solutions))
self.assertEquals(0, model.solutions[0]['x'])
self.assertEquals(0, model.solutions[0]['y'])
self.assertEquals(3.5, model.solutions[1]['x'])
self.assertEquals(5, model.solutions[1]['y'])
model = Model()
model.var('x', default=0)
model.var('y', default=0)
model.add('2*x = 12 + y')
model.add('y = if_true(x > 5)')
model.solve(iterations=10, threshold=1e-4)
self.assertEquals(2, len(model.solutions))
self.assertEquals(0, model.solutions[0]['x'])
self.assertEquals(0, model.solutions[0]['y'])
self.assertEquals(6.5, model.solutions[1]['x'])
self.assertEquals(1, model.solutions[1]['y'])
def test_get_value(self):
""" Test the get_value function """
model = Model()
varx = model.var('x', default=-1)
vary = model.var('y')
model._update_solutions({'x': 1.1, 'y': 2.2})
model._update_solutions({'x': 3.3, 'y': 4.4})
self.assertEquals(1.1, model.get_value(varx, 0))
self.assertEquals(1.1, model.get_value(varx, -2))
self.assertEquals(4.4, model.get_value(vary, 1))
self.assertEquals(4.4, model.get_value(vary, -1))
with self.assertRaises(IndexError):
self.assertEquals(-1, model.get_value(varx, -1000))
with self.assertRaises(IndexError):
self.assertEquals(-1, model.get_value(varx, 1000))
def test_model_with_function(self):
""" Test model with builtin function call test """
model = Model()
model.var('x', default=0)
model.var('y', default=0)
model.add('2*x = 12 - y')
model.add('y = if_true(x > 10) + 5')
model.solve(iterations=10, threshold=1e-4)
self.assertEquals(2, len(model.solutions))
self.assertEquals(0, model.solutions[0]['x'])
self.assertEquals(0, model.solutions[0]['y'])
self.assertEquals(3.5, model.solutions[1]['x'])
self.assertEquals(5, model.solutions[1]['y'])
model = Model()
model.var('x', default=0)
model.var('y', default=0)
model.add('2*x = 12 + y')
model.add('y = if_true(x > 5)')
model.solve(iterations=10, threshold=1e-4)
self.assertEquals(2, len(model.solutions))
self.assertEquals(0, model.solutions[0]['x'])
self.assertEquals(0, model.solutions[0]['y'])
self.assertEquals(6.5, model.solutions[1]['x'])
self.assertEquals(1, model.solutions[1]['y'])
def test_model(self):
""" Create an empty model class """
model = Model()
self.assertIsNotNone(model)
def test_evaluate_series_access(self):
""" Test evaluation with series accessor """
model = Model()
model.var('x', default=1)
model.var('y', default=10)
model.param('a', default=.5)
model.solutions = [{'x': 2, 'y': 11, 'a': 60}]
self.assertEquals(11, model.evaluate('y(-1)'))
self.assertEquals(73, model.evaluate('x(-1) + y(-1) + a(-1)'))
def create_lp_model():
""" Creates model LP """
# pylint: disable=too-many-statements
model = Model()
model.set_var_default(0)
model.var('Bcb', desc='Government bills held by the Central Bank')
model.var('Bd', desc='Demand for government bills')
model.var('Bh', desc='Government bills held by households')
model.var('Bs', desc='Government bills supplied by government')
model.var('BLd', desc='Demand for government bonds')
model.var('BLh', desc='Government bonds held by households')
model.var('BLs', desc='Supply of government bonds')
model.var('CG', desc='Capital gains on bonds')
model.var('CGe', desc='Expected capital gains on bonds')
model.var('C', desc='Consumption')
model.var('ERrbl', desc='Expected rate of return on bonds')
model.var('Hd', desc='Demand for cash')
model.var('Hh', desc='Cash held by households')
model.var('Hs', desc='Cash supplied by the central bank')
model.var('Pbl', desc='Price of bonds')
model.var('Pble', desc='Expected price of bonds')
model.var('Rb', desc='Interest rate on government bills')
model.var('Rbl', desc='Interest rate on government bonds')
model.var('T', desc='Taxes')
model.var('V', desc='Household wealth')
model.var('Ve', desc='Expected household wealth')
model.var('Y', desc='Income = GDP')
model.var('YDr', desc='Regular disposable income of households')
model.var('YDre', desc='Expected regular disposable income of households')
model.set_param_default(0)
model.param('alpha1', desc='Propensity to consume out of income')
model.param('alpha2', desc='Propensit to consume out of wealth')
model.param('chi', desc='Weight of conviction in expected bond price')
model.param('lambda10', desc='Parameter in asset demand function')
model.param('lambda12', desc='Parameter in asset demand function')
model.param('lambda13', desc='Parameter in asset demand function')
model.param('lambda14', desc='Parameter in asset demand function')
model.param('lambda20', desc='Parameter in asset demand function')
model.param('lambda22', desc='Parameter in asset demand function')
model.param('lambda23', desc='Parameter in asset demand function')
model.param('lambda24', desc='Parameter in asset demand function')
model.param('lambda30', desc='Parameter in asset demand function')
model.param('lambda32', desc='Parameter in asset demand function')
model.param('lambda33', desc='Parameter in asset demand function')
model.param('lambda34', desc='Parameter in asset demand function')
model.param('theta', desc='Tax rate')
model.param('G', desc='Government goods')
model.param('Rbar', desc='Exogenously set interest rate on govt bills')
model.param('Pblbar', desc='Exogenously set price of bonds')
model.add('Y = C + G') # 5.1
model.add('YDr = Y - T + Rb(-1)*Bh(-1) + BLh(-1)') # 5.2
model.add('T = theta *(Y + Rb(-1)*Bh(-1) + BLh(-1))') # 5.3
model.add('V - V(-1) = (YDr - C) + CG') # 5.4
model.add('CG = (Pbl - Pbl(-1))*BLh(-1)')
model.add('C = alpha1*YDre + alpha2*V(-1)')
model.add('Ve = V(-1) + (YDre - C) + CG')
model.add('Hh = V - Bh - Pbl*BLh')
model.add('Hd = Ve - Bd - Pbl*BLd')
model.add('Bd = Ve*lambda20 + Ve*lambda22*Rb - ' +
'Ve*lambda23*ERrbl - lambda24*YDre')
model.add('BLd = (Ve*lambda30 - Ve*lambda32*Rb ' +
' + Ve*lambda33*ERrbl - lambda34*YDre)/Pbl')
model.add('Bh = Bd')
model.add('BLh = BLd')
model.add('Bs - Bs(-1) = (G + Rb(-1)*Bs(-1) + ' +
'BLs(-1)) - (T + Rb(-1)*Bcb(-1)) - (BLs - BLs(-1))*Pbl')
model.add('Hs - Hs(-1) = Bcb - Bcb(-1)')
model.add('Bcb = Bs - Bh')
model.add('BLs = BLh')
model.add('ERrbl = Rbl + chi * (Pble - Pbl) / Pbl')
model.add('Rbl = 1./Pbl')
model.add('Pble = Pbl')
model.add('CGe = chi * (Pble - Pbl)*BLh')
model.add('YDre = YDr(-1)')
model.add('Rb = Rbar')
model.add('Pbl = Pblbar')
# if_true(x) returns 1 if x is true, else 0 is returned
model.add('z1 = if_true(tp > top)')
model.add('z2 = if_true(tp < bot)')
return model
def test_full_model(self):
""" Test by implementing a model
This model is taken from the book
Monetary Economics 2ed, Godley and Lavoie, 2012
Chapter 3, The Simplest Model wtih Government Money
Model SIM
"""
# pylint: disable=too-many-statements
model = Model()
model.set_var_default(0)
model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs',
'Cd', 'Ns', 'Nd')
model.set_param_default(0)
Gd = model.param('Gd')
W = model.param('W')
alpha1 = model.param('alpha1')
alpha2 = model.param('alpha2')
theta = model.param('theta')
model.add('Cs = Cd')
model.add('Gs = Gd')
model.add('Ts = Td')
model.add('Ns = Nd')
model.add('YD = (W*Ns) - Ts')
model.add('Td = theta * W * Ns')
model.add('Cd = alpha1*YD + alpha2*Hh(-1)')
model.add('Hs - Hs(-1) = Gd - Td')
model.add('Hh - Hh(-1) = YD - Cd')
model.add('Y = Cs + Gs')
model.add('Nd = Y/W')
# setup default parameter values
Gd.value = 20.
W.value = 1.0
alpha1.value = 0.6
alpha2.value = 0.4
theta.value = 0.2
model.solve(iterations=200, threshold=1e-3)
soln = round_solution(model.solutions[-1], decimals=1)
self.assertTrue(numpy.isclose(38.5, soln['Y']))
self.assertTrue(numpy.isclose(7.7, soln['Ts']))
self.assertTrue(numpy.isclose(30.8, soln['YD']))
self.assertTrue(numpy.isclose(18.5, soln['Cs']))
self.assertTrue(numpy.isclose(12.3, soln['Hs']))
self.assertTrue(numpy.isclose(12.3, soln['Hh']))
model.solve(iterations=200, threshold=1e-3)
soln = round_solution(model.solutions[-1], decimals=1)
self.assertTrue(numpy.isclose(47.9, soln['Y']))
self.assertTrue(numpy.isclose(9.6, soln['Ts']))
self.assertTrue(numpy.isclose(38.3, soln['YD']))
self.assertTrue(numpy.isclose(27.9, soln['Cs']))
self.assertTrue(numpy.isclose(22.7, soln['Hs']))
self.assertTrue(numpy.isclose(22.7, soln['Hh']))
# Now run until the solutions themselves converge
prev_soln = model.solutions[-1]
converges = False
for _ in xrange(100):
model.solve(iterations=100, threshold=1e-3)
# run until we converge
soln = model.solutions[-1]
if is_close(prev_soln, soln, atol=1e-3):
converges = True
break
prev_soln = soln
self.assertTrue(converges)
prev = round_solution(model.solutions[-2], decimals=1)
soln = round_solution(model.solutions[-1], decimals=1)
self.assertTrue(numpy.isclose(100, soln['Y']))
self.assertTrue(numpy.isclose(20, soln['Ts']))
self.assertTrue(numpy.isclose(80, soln['YD']))
self.assertTrue(numpy.isclose(80, soln['Cs']))
self.assertTrue(numpy.isclose(0, soln['Hs'] - prev['Hs']))
self.assertTrue(numpy.isclose(0, soln['Hh'] - prev['Hh']))
def test_get_value(self):
""" Test the get_value function """
model = Model()
varx = model.var('x', default=-1)
vary = model.var('y')
model._update_solutions({'x': 1.1, 'y': 2.2})
model._update_solutions({'x': 3.3, 'y': 4.4})
self.assertEquals(1.1, model.get_value(varx, 0))
self.assertEquals(1.1, model.get_value(varx, -2))
self.assertEquals(4.4, model.get_value(vary, 1))
self.assertEquals(4.4, model.get_value(vary, -1))
with self.assertRaises(IndexError):
self.assertEquals(-1, model.get_value(varx, -1000))
with self.assertRaises(IndexError):
self.assertEquals(-1, model.get_value(varx, 1000))
def create_sim_model():
model = Model()
model.set_var_default(0)
model.var('Cd', desc='Consumption goods demand by households')
model.var('Cs', desc='Consumption goods supply')
model.var('Gs', desc='Government goods, supply')
model.var('Hh', desc='Cash money held by households')
model.var('Hs', desc='Cash money supplied by the government')
model.var('Nd', desc='Demand for labor')
model.var('Ns', desc='Supply of labor')
model.var('Td', desc='Taxes, demand')
model.var('Ts', desc='Taxes, supply')
model.var('Y', desc='Income = GDP')
model.var('YD', desc='Disposable income of households')
model.param('Gd', desc='Government goods, demand')
model.param('W', desc='Wage rate')
model.param('alpha1', desc='Propensity to consume out of income')
model.param('alpha2', desc='Propensity to consume out of wealth')
model.param('theta', desc='Tax rate')
model.add('Cs = Cd') # 3.1
model.add('Gs = Gd') # 3.2
model.add('Ts = Td') # 3.3
model.add('Ns = Nd') # 3.4
model.add('YD = (W*Ns) - Ts') # 3.5
model.add('Td = theta * W * Ns') # 3.6, theta < 1.0
model.add('Cd = alpha1*YD + alpha2*Hh(-1)') # 3.7, 0 < alpha2 < alpha1 < 1
model.add('Hs - Hs(-1) = Gd - Td') # 3.8
model.add('Hh - Hh(-1) = YD - Cd') # 3.9
model.add('Y = Cs + Gs') # 3.10
model.add('Nd = Y/W') # 3.11
return model
def create_model():
""" Creates model SIM """
model = Model()
model.set_var_default(0)
model.var('Cd', desc='Consumption goods demand by households')
model.var('Cs', desc='Consumption goods supply')
model.var('Gs', desc='Government goods, supply')
model.var('Hh', desc='Cash money held by households')
model.var('Hs', desc='Cash money supplied by the government')
model.var('Nd', desc='Demand for labor')
model.var('Ns', desc='Supply of labor')
model.var('Td', desc='Taxes, demand')
model.var('Ts', desc='Taxes, supply')
model.var('Y', desc='Income = GDP')
model.var('YD', desc='Disposable income of households')
# This is a shorter way to declare multiple variables
# model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs',
# 'Cd', 'Ns', 'Nd')
model.param('Gd', desc='Government goods, demand', default=20)
model.param('W', desc='Wage rate', default=1)
model.param('alpha1',
desc='Propensity to consume out of income',
default=0.6)
model.param('alpha2',
desc='Propensity to consume o of wealth',
default=0.4)
model.param('theta', desc='Tax rate', default=0.2)
model.add('Cs = Cd')
model.add('Gs = Gd')
model.add('Ts = Td')
model.add('Ns = Nd')
model.add('YD = (W*Ns) - Ts')
model.add('Td = theta * W * Ns')
model.add('Cd = alpha1*YD + alpha2*Hh(-1)')
model.add('Hs - Hs(-1) = Gd - Td')
model.add('Hh - Hh(-1) = YD - Cd')
model.add('Y = Cs + Gs')
model.add('Nd = Y/W')
return model
